Some optimal problems in reactor kinetics
Izvestiya. Mathematics , Tome 11 (1977) no. 5, pp. 1119-1148.

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In this paper the authors present a method of studying distributed parameter optimal problems in the theory of nuclear reactors, connected with an integro-differential system of equations for reactor kinetics. Two basic nonstationary optimal problems are considered: a problem with fixed control time and a time-optimal problem. For both problems necessary conditions are derived for optimality of admissible control elements. Bibliography: 27 titles.
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Yu. A. Kuznetsov; S. F. Morozov. Some optimal problems in reactor kinetics. Izvestiya. Mathematics , Tome 11 (1977) no. 5, pp. 1119-1148. http://geodesic.mathdoc.fr/item/IM2_1977_11_5_a11/

[1] Kliger I., “Optimalnoe po bystrodeistviyu upravlenie yadernym reaktorom”, Avtomaticheskoe upravlenie teplovymi i khimicheskimi protsessami (Tr. III Mezhdunarodnogo kongressa Mezhdunarodnoi federatsii po avtomaticheskomu upravleniyu, 1966), Nauka, M., 1972, 126–137

[2] Moon S. F., Mohler R. R., “Reactivity-rate constrained time optimal neutron kinetics”, Nucl. Sci. and Engng., 36:1 (1969), 125–128

[3] Lewins M. J., Williamson T. J., Babb A. L., “Energy optimal xenon shutdown trajectories”, Trans. Amer. Nucl. Soc., 9:1 (1966), 281–282

[4] Lewins M. J., Woodcock G. R., Williamson T. J., Babb A. L., “Energy optimal xenon shutdown”, Nucl. Sci. and Engng., 31:2 (1968), 272–281

[5] Kyong S. H., “An optimal control of a distributed parameter reactor”, Nucl. Sci. and Engng., 32:1 (1968), 146–149

[6] Roberts J. J., Smith H. P. Jr., “Time optimal solution to the reactivity-xenon shutdown problem”, Nucl. Sci. and Engng., 22:4 (1965), 470–478

[7] El-Bassioni A. A., Poncelet C. G., “Minimal time control of spatial xenon oscillations in nuclear power reactors”, Nucl. Sci. and Engng., 54:2 (1974), 166–176

[8] Wiberg D. M., “Optimal control of nuclear reactor systems”, Advances in Control System Theory and Applications, V, Academic Press, 1967, 301–388

[9] Ash M., Optimal shutdown control of nuclear reactors, Academic Press, New York, London, 1966

[10] Weaver L. E., Reactors dynamics and control, Elsevier, New York, London, Amsterdam, 1968

[11] Mohler R. R., Shen C. N., “Optimal control of nuclear reactors”, Nucl. Sci. and Technology, 6, Academic Press, New York, London, 1970

[12] Rudik A. P., Yadernye reaktory i printsip maksimuma Pontryagina, Atomizdat, M., 1971

[13] Osnovy avtomaticheskogo upravleniya yadernymi kosmicheskimi energeticheskimi ustanovkami, ed. B. N. Petrov, Mashinostroenie, M., 1974

[14] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1969

[15] Plotnikov V. I., “Neobkhodimye i dostatochnye usloviya optimalnosti i usloviya edinstvennosti optimiziruyuschikh funktsii dlya upravlyaemykh sistem obschego vida”, Izv. AN SSSR. Ser. matem., 36 (1972), 652–679 | MR | Zbl

[16] Kuznetsov Yu. A., Morozov S. F., “Korrektnost postanovki smeshannoi zadachi dlya nestatsionarnogo uravneniya perenosa”, Differentsialnye uravneniya, 8:9 (1972), 1639–1648 | MR | Zbl

[17] Kuznetsov Yu. A., Morozov S. F., “Integro-differentsialnaya sistema uravnenii kinetiki reaktora”, Differentsialnye uravneniya, 10:8 (1974), 1491–1503 | Zbl

[18] Kuznetsov Yu. A., Morozov S. F., “Matematicheskie zadachi kinetiki reaktora”, Dokl. AN SSSR, 218:3 (1974), 543–546

[19] Kuznetsov Yu. A., Morozov S. F., “O neobkhodimykh usloviyakh optimalnosti v zadachakh upravleniya protsessami perenosa”, Prikladn. matematika i mekhanika, 38:2 (1974), 290–300 | MR | Zbl

[20] Morozov S. F., Sumin V. I., “Ob odnoi zadache optimalnogo upravleniya nestatsionarnymi protsessami perenosa”, Differentsialnye uravneniya, 8:12 (1972), 2235–2243 | MR | Zbl

[21] Morozov S. F., Sumin V. I., “Neobkhodimye usloviya optimalnosti dlya upravlyaemykh statsionarnykh protsessov perenosa”, Izv. VUZov, Matematika, 1974, no. 10, 46–56 | MR | Zbl

[22] Kuznetsov Yu. A., Morozov S. F., “Nekotorye optimalnye zadachi kinetiki reaktorov”, Dokl. AN SSSR, 226:4 (1976), 791–794 | MR | Zbl

[23] Usachev L. N., “Uravnenie dlya tsennosti neitronov, kinetika reaktora i teoriya vozmuschenii”, Reaktorostroenie i teoriya reaktorov, AN SSSR, M., 1955, 251–268

[24] Koen E. R., “Nekotorye voprosy kinetiki reaktorov”, Trudy Vtoroi mezhdunarodnoi konferentsii po mirnomu ispolzovaniyu atomnoi energii, Izbrannye doklady inostrannykh uchenykh, t. 3 (Zheneva, 1958), Atomizdat, M., 1959, 549

[25] Kipin Dzh. R., Fizicheskie osnovy kinetiki yadernykh reaktorov, Atomizdat, M., 1967

[26] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, gl. V, Nauka, M., 1964 | MR

[27] Vladimirov V. S., “Matematicheskie zadachi odnoskorostnoi teorii perenosa chastits”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 61, 1961, 3–158 | MR